More concerning the anelastic and subseismic approximations for low-frequency modes in stars

Two approximations, namely the subseismic approximation and the anelastic approximation, are presently used to filter out the acoustic modes when computing low frequency modes of a star (gravity modes or inertial modes). In a precedent paper (Dintrans & Rieutord 2001), we observed that the anelastic approximation gave eigenfrequencies much closer to the exact ones than the subseismic approximation. Here, we try to clarify this behaviour and show that it is due to the different physical approach taken by each approximation: On the one hand, the subseismic approximation considers the low frequency part of the spectrum of (say) gravity modes and turns out to be valid only in the central region of a star; on the other hand, the anelastic approximation considers the Brunt-Vaisala frequency as asymptotically small and makes no assumption on the order of the modes. Both approximations fail to describe the modes in the surface layers but eigenmodes issued from the anelastic approximation are closer to those including acoustic effects than their subseismic equivalent. We conclude that, as far as stellar eigenvalue problems are concerned, the anelastic approximation is better suited for simplifying the eigenvalue problem when low-frequency modes of a star are considered, while the subseismic approximation is a useful concept when analytic solutions of high order low-frequency modes are needed in the central region of a star.Comment: 5 pages 3 fig, to appear in MNRA

Identification of gravity waves in hydrodynamical simulations

The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated velocity field onto the anelastic solutions of the linear eigenvalue problem for the perturbations. This facilitates a quantitative study of both the spectrum and the amplitudes of excited g-modes.Comment: 12 pages, 11 figures, Appendices only available onlin

Numerical simulations of the kappa-mechanism with convection

A strong coupling between convection and pulsations is known to play a major role in the disappearance of unstable modes close to the red edge of the classical Cepheid instability strip. As mean-field models of time-dependent convection rely on weakly-constrained parameters, we tackle this problem by the means of 2-D Direct Numerical Simulations (DNS) of kappa-mechanism with convection. Using a linear stability analysis, we first determine the physical conditions favourable to the kappa-mechanism to occur inside a purely-radiative layer. Both the instability strips and the nonlinear saturation of unstable modes are then confirmed by the corresponding DNS. We next present the new simulations with convection, where a convective zone and the driving region overlap. The coupling between the convective motions and acoustic modes is then addressed by using projections onto an acoustic subspace.Comment: 5 pages, 6 figures, accepted for publication in Astrophysics and Space Science, HELAS workshop (Rome june 2009

Convective quenching of stellar pulsations

Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of the convection-pulsation coupling, in which the oscillations are sustained by a continuous physical process: the kappa-mechanism. Thanks to both a frequential analysis and a projection of the physical fields onto an acoustic subspace, we study how the convective motions affect the unstable radial oscillations. Results: depending on the initial physical conditions, two main behaviours are obtained: (i) either the unstable fundamental acoustic mode has a large amplitude, carries the bulk of the kinetic energy and shows a nonlinear saturation similar to the purely radiative case; (ii) or the convective motions affect significantly the mode amplitude that remains very weak. In this second case, convection is quenching the acoustic oscillations. We interpret these discrepancies in terms of the difference in density contrast: larger stratification leads to smaller convective plumes that do not affect much the purely radial modes, while large-scale vortices may quench the oscillations.Comment: 15 pages, 17 figures, 3 tables, accepted for publication in A&

Testing turbulent closure models with convection simulations

We compare simple analytical closure models of homogeneous turbulent Boussinesq convection for stellar applications with three-dimensional simulations. We use simple analytical closure models to compute the fluxes of angular momentum and heat as a function of rotation rate measured by the Taylor number. We also investigate cases with varying angles between the angular velocity and gravity vectors, corresponding to locating the computational domain at different latitudes ranging from the pole to the equator of the star. We perform three-dimensional numerical simulations in the same parameter regimes for comparison. The free parameters appearing in the closure models are calibrated by two fitting methods using simulation data. Unique determination of the closure parameters is possible only in the non-rotating case or when the system is placed at the pole. In the other cases the fit procedures yield somewhat differing results. The quality of the closure is tested by substituting the resulting coefficients back into the closure model and comparing with the simulation results. To eliminate the possibilities that the results obtained depend on the aspect ratio of the simulation domain or suffer from too small Rayleigh numbers we performed runs varying these parameters. The simulation data for the Reynolds stress and heat fluxes broadly agree with previous compressible simulations. The closure works fairly well with slow and fast rotation but its quality degrades for intermediate rotation rates. We find that the closure parameters depend not only on rotation rate but also on latitude. The weak dependence on Rayleigh number and the aspect ratio of the domain indicates that our results are generally validComment: 21 pages, 9 figures, submitted to Astron. Nach

Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincar\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\'egime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.Comment: 4 pages, 5 fi

Shearing and embedding box simulations of the magnetorotational instability

Two different computational approaches to the magnetorotational instability (MRI) are pursued: the shearing box approach which is suited for local simulations and the embedding box approach whereby a Taylor Couette flow is embedded in a box so that numerical problems with the coordinate singularity are avoided. New shearing box simulations are presented and differences between regular and hyperviscosity are discussed. Preliminary simulations of spherical nonlinear Taylor Couette flow in an embedding box are presented and the effects of an axial field on the background flow are studied.Comment: to appear in "Hydromagnetic rotating-flow experiments", eds. A. Bonanno, AI